The notion that trade and capital flows drive exchange rates is widespread in the financial press but receives scant attention in economic research. The flow market model of the exchange rate has fallen out of fashion in the 1970s, at a time when stock-oriented approaches, such as monetary and portfolio balance models, gained prominence. However, given the limited empirical success of mainstream exchange rate models over the past decades, it may be time for a reassessment of the flow market approach. The aim of this work is to demonstrate how balance of payments imbalances influence the demands for different currencies in the foreign exchange markets over time. A dynamical system approach is used to assess how international payments evolve for different sets of assumptions regarding the joint dynamic behaviour of various balance of payments components. An important finding is that while the different components of the balance of payments affect international payment flows directly in a given country, they also determine the accumulation of foreign assets and liabilities in that country, or its international investment position. However, the international investment position itself gives rise to international payments, for instance when foreign debt becomes due and is repaid or when interest payments on the existing debt stock are made. The dynamical system approach is further applied to topics such as currency crises and the exchange rate performance of commodity exporters. Two empirical essays on the important case of Japan confirm the above hypotheses. The first essay builds a vector error correction model for the nominal exchange rate and the current account in Japan. The model allows for a Markov-switching stochastic trend in the current account. The model is capable of producing the strong cycles of the current account and the gradual adjustment of the exchange rate, which can both be observed in the Japanese data. Bayesian estimation proceeds using an innovative Gibbs sampling procedure. The second essay estimates the maturity structure of Japan's foreign lending. It constructs an explicit measure of cross-border payment flows across Japanese borders, based on the estimated maturity structure of Japan's foreign lending. The simulated cross-border payment flows are shown to closely follow the movements of the Japanese exchange rate. An additional empirical essay considers the reverse question of how the current account is influenced by exchange rate fluctuations. Based on German and Japanese data, it is shown that strong exchange rate movements have tended to influence the trend of the current account, rather than its level as is typically assumed in the literature.